On the convergence of difference schemes for one nonlocal boundary-value problem

Polynomial-based mean weighted residuals methods for elliptic problems with nonlocal boundary conditions in the rectangle

“…Similar problems have been studied in [24][25][26] and references therein. Actually, some theoretical results obtained in [24,27] can be used partially to study the existence and uniqueness of the weak solution of the variational problem associated to (1)- (4) or (1)- (3) and (5).…”

“…c Vilnius University, 2014 Finite difference schemes for two-dimensional elliptic problems with nonlocal boundary conditions were considered in [13][14][15] and references therein. In [16,17], the solvability of the finite difference schemes for a similar problem was proved and the discretization error estimates were obtained. Some error estimates on the finite element approximation for two-dimensional elliptic problem with nonlocal boundary conditions were given in [18].…”

A survey on stationary problems, Green's functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions

“…The paper of D. Gordeziani, E. Gordeziani, Davitashvili and Meladze [53] deals with the formulation and analysis of a generalized nonlocal problem for the elliptic equations with variable coefficients. Berikelashvili and Khomeriki in [15,16] Rassias and Karimov investigated some BVPs with nonlocal initial condition for model and degenerate parabolic equations with parameter [162]. Karatay, Bayramoglu, Yildiz and Kokluce study matrix stability of the first-order and the second-order FDS for parabolic BVPs with NBCs [110].…”

“…Berikelashvili and Khomeriki consider the Poisson equation in a rectangular domain with an integral constraints [17]. The corresponding FDS scheme is constructed.…”

A fourth-order accurate difference Dirichlet problem for the approximate solution of Laplace’s equation with integral boundary condition

“…Different finite-difference problems as approximations of the nonlocal problems with integral boundary condition have been studied by many authors (see [1][2][3][4][5] and references given therein). They all were basically focusing on the following difficulties related to the existence of a quadrature approximation of the integral condition on the side of the domain where nonlocal condition was given: (i) finding an approximate solution by solving the obtained system of equations which are non-band matrices, (ii) determining the rate of convergence of the approximate solution by appropriate smoothness conditions on the given data.…”